Global existence of smooth solutions for three-dimensional magnetic Bénard system with mixed partial dissipation, magnetic diffusion and thermal diffusivity

This paper deals with the Cauchy problem to the 3D system of incompressible magnetic Bénard fluids. We prove that as the initial data satisfy ‖u0‖H1(R3)2+‖b0‖H1(R3)2+‖θ0‖H1(R3)2≤ε, where ε is a suitably small positive number, then the 3D magnetic Bénard system with mixed partial dissipation, magnetic diffusion and thermal diffusivity admit global smooth solutions.